Variable neighbourhood search for dual-resource constrained flexible job shop scheduling

Dual-resource constrained flexible job shop scheduling problem (FJSP) is considered and an effective variable neighbourhood search (VNS) is presented, in which the solution to the problem is indicated as a quadruple string of the ordered operations and their resources. Two neighbourhood search procedures are sequentially executed to produce new solutions for two sub-problems of the problem, respectively. The search of VNS is restarted from a slightly perturbed version of the current solution of VNS when the determined number of iterations is reached. VNS is tested on some instances and compared with methods from literature. Computational results show the significant advantage of VNS on the problem.     

A variable neighbourhood search algorithm for the flexible job-shop scheduling problem

The flexible job-shop scheduling problem (FJSP) is a generalisation of the classical job-shop scheduling problem which allows an operation of each job to be executed by any machine out of a set of available machines. FJSP consists of two sub-problems which are assigning each operation to a machine out of a set of capable machines (routing sub-problem) and sequencing the assigned operations on the machines (sequencing sub-problem). This paper proposes a variable neighbourhood search (VNS) algorithm that solves the FJSP to minimise makespan. In the process of the presented algorithm, various neighbourhood structures related to assignment and sequencing problems are used for generating neighbouring solutions. To compare our algorithm with previous ones, an extensive computational study on 181 benchmark problems has been conducted. The results obtained from the presented algorithm are quite comparable to those obtained by the best-known algorithms for FJSP.     

Robust scheduling for multi-objective flexible job-shop problems with flexible workdays

This study determines a robust schedule for a flexible job-shop scheduling problem with flexible workdays. The performance criteria considered in this study are tardiness, overtime and robustness. Furthermore, the problem is addressed in a Pareto manner, and a set of Pareto-optimal solutions is determined for this purpose. In consideration of all the aforementioned features, a goal-guided neighbourhood function is proposed based on efficient problem-dependent move-filtering methods. Two metaheuristic algorithms, named goal-guided multi-objective tabu search and goal-guided multi-objective hybrid search, are proposed in this work based on this neighbourhood function. The effectiveness of these approaches is demonstrated via empirical studies.     

Flexible job shop with continuous material flow

A new scheduling problem, the continuous flow flexible job shop (CF-FJS) is proposed. The formulation combines the well-known flexible job shop (FJS) problem and a dedicated continuous material flow model (MFM). In the MFM, operations are represented by material flow functions derived by integration of arbitrarily defined speed patterns. Two main concepts of the MFM formalism, i.e. variable speed of processing and continuous material flow, lead to position-dependent processing times and overlapping in operations which extend standard FJS formulation. Properties of the CF-FJS are investigated. A tabu search sched uling algorithm utilising these properties is proposed. Effective neighbourhood functions are defined based on elimination approaches. Two auxiliary procedures: search intensification level switching and fast feasibility detection are added to improve algorithm efficiency. The algorithm is verified using dedicated benchmark instances which comprise non-trivial representations of the CF-FJS specific features, i.e. machine efficiency patterns and minimum inter-operation buffers. The research is motivated by task scheduling in a fastener factory, but the presented results can be useful in many domains, such as production of granular goods, steel details, glass and fluids. The solution can be used in real-world applications. The published results can be helpful in testing new CF-FJS scheduling algorithms.     

改进遗传算法解决柔性作业车间调度问题

柔性作业车间调度问题是经典作业车间调度问题的扩展,它允许工序在多台机器中的任意一台上加工.针对柔性作业车间调度问题的特点,提出一种扩展的基于工序的编码及其主动调度的解码机制,并设计一种初始解产生机制和两种有效的交叉和变异操作.为了克服传统遗传算法早熟和收敛慢的缺点,设计了精英解保留策略和子代产生模式结合的改进遗传算法应用于该调度问题.最后运用提出的算法求解基准测试问题验证算法的有效性.     

A hybrid algorithm for total tardiness minimisation in flexible job shop: genetic algorithm with parallel VNS execution

This paper addresses the flexible-job-shop scheduling problem (FJSP) with the objective of minimising total tardiness. FJSP is the generalisation of the classical job-shop scheduling problem. The difference is that in the FJSP problem, the operations associated with a job can be processed on any set of alternative machines. We developed a new algorithm by hybridising genetic algorithm and variable neighbourhood search (VNS). The genetic algorithm uses advanced crossover and mutation operators to adapt the chromosome structure and the characteristics of the problem. Parallel-executed VNS algorithm is used in the elitist selection phase of the GA. Local search in VNS uses assignment of operations to alternative machines and changing of the order of the selected operation on the assigned machine to increase the result quality while maintaining feasibility. The purpose of parallelisation in the VNS algorithm is to minimise execution time. The performance of the proposed method is validated by numerical experiments on several representative problems and compared with adapted constructive heuristic algorithms’ (earliest due date, critical ratio and slack time per remaining operation) results.     

Scheduling flexible manufacturing cells using Tabu Search

Scheduling is an important aspect in the overall control of a flexible manufacturing system. The research presented focuses on production scheduling of jobs within a flexible manufacturing cell (FMC)–one type of flexible manufacturing system. Due to the complexity of the FMC scheduling problem, a 0–1 mixed-integer linear programming (MILP) model is formulated for M machines and N jobs with alternative routings. Although small instances of the problem can be solved optimally with MILP models, a two-stage Tabu Search (TS² ) algorithm that minimises the manufacturing makespan (MS) is proposed to solve medium-to-large-scale problems more efficiently. During Stage I (construction phase), two heuristics are utilised to generate an initial feasible sequence and an initial MS solution. In Stage II (improvement phase), the acquired initial solutions from Stage I are combined with a Tabu Search meta-heuristic procedure that provides improved MS solutions. The TS² algorithm provides tremendous savings in computational time for medium/large-sized multi-machine FMC problems.     

A filtered-beam-search-based heuristic algorithm for flexible job-shop scheduling problem

Scheduling for the flexible job-shop is a very important issue in both fields of combinatorial optimization and production operations. However, due to combination of the routing and sequencing problems, flexible job-shop scheduling problem (FJSP) presents additional difficulty than the classical job-shop scheduling problem and requires more effective algorithms. This paper developed a filtered-beam-search-based heuristic algorithm (named as HFBS) to find sub-optimal schedules within a reasonable computational time for the FJSP with multiple objectives of minimising makespan, the total workload of machines and the workload of the most loaded machine. The proposed algorithm incorporates dispatching rules based heuristics and explores intelligently the search space to avoid useless paths, which makes it possible to improve the search speed. Through computational experiments, the performance of the presented algorithm is evaluated and compared with those of existing literature and those of commonly used dispatching rules, and the results demonstrate that the proposed algorithm is an effective and practical approach for the FJSP.     

A hybrid artificial bee colony algorithm for flexible job shop scheduling with worker flexibility

The traditional flexible job shop scheduling problem (FJSP) considers machine flexibility but not worker flexibility. Given the influence and potential of human factors in improving production efficiency and decreasing the cost in practical production systems, we propose a mathematical model of an extended FJSP with worker flexibility (FJSPW). A hybrid artificial bee colony algorithm (HABCA) is presented to solve the proposed FJSPW. For the HABCA, effective encoding, decoding, crossover and mutation operators are designed, and a new effective local search method is developed to improve the speed and exploitation ability of the algorithm. The Taguchi method of Design of Experiments is used to obtain the best combination of key parameters of the HABCA. Extensive computational experiments carried out to compare the HABCA with some well-performing algorithms from the literature confirm that the proposed HABCA is more effective than these algorithms, especially on large-scale FJSPW instances.     

A hybrid artificial bee colony algorithm for a flexible job shop scheduling problem with overlapping in operations

Overlapping in operations is an effective technology for productivity improvement in modern manufacturing systems. Thus far, however, there are still rare works on flexible job shop scheduling problems (FJSPs) concerning this strategy. In this paper, we present a hybrid artificial bee colony (hyABC) algorithm to minimise the total flowtime for a FJSP with overlapping in operations. In the proposed hyABC, a dynamic scheme is introduced to fine-tune the search scope adaptively. In view of poor exploitation ability of artificial bee colony algorithm, a modified migrating birds optimisation algorithm (MMBO) is developed and integrated into the search process for better balancing global exploration and local exploitation. In MMBO, a forward share strategy with one-job based crossover is designed to make good use of valuable information from behind solutions. Besides, an improved downward share scheme is adopted to increase diversification of the population, and thus alleviate the premature convergence. Extensive experiments based on benchmark instances with different scales are carried out and comparisons with other recent algorithms identify the effectiveness of the proposed hyABC.     

An effective discrete harmony search algorithm for flexible job shop scheduling problem with fuzzy processing time

This study addresses flexible job shop scheduling problem (FJSP) with fuzzy processing time. The fuzzy or uncertainty of processing time is one of seven characteristics in remanufacturing. A discrete harmony search (DHS) algorithm is proposed for FJSP with fuzzy processing time. The objective is to minimise maximum fuzzy completion time. A simple and effective heuristic rule is proposed to initialise harmony population. Extensive computational experiments are carried out using five benchmark cases with eight instances from remanufacturing. The proposed heuristic rule is evaluated using five benchmark cases. The proposed DHS algorithm is compared to six metaheuristics. The results and comparisons show the effectiveness and efficiency of DHS for solving FJSP with fuzzy processing time.     

A hybrid water flow algorithm for multi-objective flexible flow shop scheduling problems

In this article, the multi-objective flexible flow shop scheduling problem with limited intermediate buffers is addressed. The objectives considered in this problem consist of minimizing the completion time of jobs and minimizing the total tardiness time of jobs. A hybrid water flow algorithm for solving this problem is proposed. Landscape analysis is performed to determine the weights of objective functions, which guide the exploration of feasible regions and movement towards the optimal Pareto solution set. Local and global neighbourhood structures are integrated in the erosion process of the algorithm, while evaporation and precipitation processes are included to enhance the solution exploitation capability of the algorithm in unexplored neighbouring regions. An improvement process is used to reinforce the final Pareto solution set obtained. The performance of the proposed algorithm is tested with benchmark and randomly generated instances. The computational results and comparisons demonstrate the effectiveness and efficiency of the proposed algorithm.     

混合工作日历下批量生产柔性作业车间多目标调度方法

提出了一种混合工作日历下批量生产柔性作业车间多目标调度方法。考虑设备的混合工作日历约束,构建了以生产周期最短、制造成本最低为优化目标的批量生产柔性作业车间多目标调度模型。设计了一种带精英策略的非支配排序遗传算法(NSGA II)求解该模型。算法中,采用“基于工序和设备的分段编码”方式分别对工序和设备进行编码;采用“基于工序和设备的分段交叉和变异方式”进行交叉和变异操作,采用“遗传算子改进策略”保证交叉、变异后子代个体的可行性;解码操作采用“基于平顺移动的原理”和“基于工作日历的时间推算技术”推算工序的调整开始、调整结束、加工开始和加工结束时刻。最后,通过案例分析验证了所提方法的有效性。     

Jobshop lot streaming with routing flexibility,sequence-dependent setups,machine release dates and lag time

Lot streaming is a technique of splitting production lots into smaller sublots in a multi-stage manufacturing system so that operations of a given lot can overlap. This technique can reduce the manufacturing makespan and is an effective tool in time-based manufacturing. Research on lot streaming models and solution procedures for flexible jobshops has been limited. The flexible jobshop scheduling problem is an extension of the classical jobshop scheduling problem by allowing an operation to be assigned to one of a set of eligible machines during scheduling. In this paper we develop a lot streaming model for a flexible jobshop environment. The model considers several pragmatic issues such as sequence-dependent setup times, the attached or detached nature of the setups, the machine release date and the lag time. In order to solve the developed model efficiently, an island-model parallel genetic algorithm is proposed. Numerical examples are presented to demonstrate the features of the proposed model and compare the computational performance of the parallel genetic algorithm with the sequential algorithm. The results are very encouraging.     

A hybrid electromagnetism-like algorithm for two-stage assembly flow shop scheduling problem

This paper presents a study on the two-stage assembly flow shop scheduling problem for minimising the weighed sum of maximum makespan, earliness and lateness. There are m machines at the first stage, each of which produces a component of a job. A single machine at the second stage assembles the m components together to complete the job. A novel model for solving the scheduling problem is built to optimise the maximum makespan, earliness and lateness simultaneously. Two optimal operation sequences of jobs are determined and verified. As the problem is known to be NP-hard, a hybrid variable neighbourhood search – electromagnetism-like mechanism (VNS-EM) algorithm is proposed for its handling. To search beyond local optima for a global one, VNS algorithm is embedded in each iteration of EM, whereby the fine neighbourhood search of optimum individuals can be realised and the solution is thus optimised. Simulation results show that the proposed hybrid VNS-EM algorithm outperforms the EM and VNS algorithms in both average value and standard deviation.     

A shuffled frog-leaping algorithm for flexible job shop scheduling with the consideration of energy consumption

Flexible job shop scheduling problem (FJSP) has been extensively investigated and objectives are often related to time. Energy-related objective should be considered fully in FJSP with the advent of green manufacturing. In this study, FJSP with the minimisation of workload balance and total energy consumption is considered and the conflicting between two objectives is analysed. A shuffled frog-leaping algorithm (SFLA) is proposed based on a three-string coding approach. Population and a non-dominated set are used to construct memeplexes according to tournament selection and the search process of each memeplex is done on its non-dominated member. Extensive experiments are conducted to test the search performance of SFLA and computational results show the conflicting between two objectives of FJSP and the promising advantages of SFLA on the considered FJSP.     

Hybrid algorithm based on improved extended shifting bottleneck procedure and GA for assembly job shop scheduling problem

With the makespan as the optimisation goal, we propose a hybrid solving method that combines improved extended shifting bottleneck procedure (i-ESB) and genetic algorithm (GA) for the assembly job shop scheduling problem (AJSSP). Hybrid genetic algorithm (HGA) uses a GA based on operation constraint chain coding to achieve global search and a local search based on an i-ESB. In the design of i-ESB, an extended disjunctive graph model (EDG) corresponding to AJSSP is presented. The calculation method of the operation head and tail length based on EDG is studied, as well as the searching method of key operations. The Schrage algorithm with disturbance is used to solve the single-machine scheduling subproblem. The selection criterion for bottleneck machines is increased. A greedy bottleneck machine re-optimisation process is designed. The effectiveness and superiority of the proposed algorithm are verified by testing and analysing the relevant examples in the literature.     

Flexible job-shop scheduling problem with resource recovery constraints

In this work, we introduce a Flexible Job-shop Scheduling Problem with Resource Recovery Constraints (FRRC). In the FRRC, besides the constraints of the classical Flexible Job-shop Scheduling Problem (FJSP), operations may require resources to be processed. The resources are available in batches and a recovery time is required between each batch. This problem is inspired by a real situation faced by a brewing company where different yeasts are available in a limited quantity and are recovered only once they have been completely used. The objective is to schedule the operations such that the makespan is minimised. A mathematical model and a metaheuristic based on a General Variable Neighborhood Search is proposed for the solution of the FRRC. Computational results over a large set of instances, adapted from the FJSP literature, are presented.     

A heuristic model for dynamic flexible job shop scheduling problem considering variable processing times

In real scheduling problems, unexpected changes may occur frequently such as changes in task features. These changes cause deviation from primary scheduling. In this article, a heuristic model, inspired from Artificial Bee Colony algorithm, is proposed for a dynamic flexible job-shop scheduling (DFJSP) problem. This problem consists of n jobs that should be processed by m machines and the processing time of jobs deviates from estimated times. The objective is near-optimal scheduling after any change in tasks in order to minimise the maximal completion time (Makespan). In the proposed model, first, scheduling is done according to the estimated processing times and then re-scheduling is performed after determining the exact ones considering machine set-up. In order to evaluate the performance of the proposed model, some numerical experiments are designed in small, medium and large sizes in different levels of changes in processing times and statistical results illustrate the efficiency of the proposed algorithm.     

Learning dispatching rules using random forest in flexible job shop scheduling problems

In this paper, we address the flexible job-shop scheduling problem (FJSP) with release times for minimising the total weighted tardiness by learning dispatching rules from schedules. We propose a random-forest-based approach called Random Forest for Obtaining Rules for Scheduling (RANFORS) in order to extract dispatching rules from the best schedules. RANFORS consists of three phases: schedule generation, rule learning with data transformation, and rule improvement with discretisation. In the schedule generation phase, we present three solution approaches that are widely used to solve FJSPs. Based on the best schedules among them, the rule learning with data transformation phase converts them into training data with constructed attributes and generates a dispatching rule with inductive learning. Finally, the rule improvement with discretisation improves dispatching rules with a genetic algorithm by discretising continuous attributes and changing parameters for random forest with the aim of minimising the average total weighted tardiness. We conducted experiments to verify the performance of the proposed approach and the results showed that it outperforms the existing dispatching rules. Moreover, compared with the other decision-tree-based algorithms, the proposed algorithm is effective in terms of extracting scheduling insights from a set of rules.